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2007

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Articles 421 - 450 of 541

Full-Text Articles in Mathematics

Numerical Approximations Of Differential Equations And Applications In Maple, Joyce Zimmerman Jan 2007

Numerical Approximations Of Differential Equations And Applications In Maple, Joyce Zimmerman

Masters Theses

The primary purpose of this work was as an aid for students taking an elemenentary differential equations course, or for students that may be trying to find approximate solutions to a differential equation without solving it. This work covers numererical methods of approximating differential equations. There are three types of methods covered, Euler's method, Runge-Kutta method, and Picard method. Also, in each of these sections there is a biography to introduce students to the various mathematicians covered. In the Appendix, there are several Maple worksheets that can be implemented into a differential equations course. These worksheets contain some programming language …

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Casimir Effect In Quantum Physics, Matthew James Urfer Jan 2007

Casimir Effect In Quantum Physics, Matthew James Urfer

Masters Theses

The Casimir Effect while over 60 years old, still holds profound implications for several branches of Physics, including but not limited too, Quantum Field Theory, Mathematical Physics, and Cosmology. This paper offers a review of Casimir Physics in regard to Quantum Physics.

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On Cosmall Abelian Groups, Brendan Goldsmith, O. Kolman Jan 2007

On Cosmall Abelian Groups, Brendan Goldsmith, O. Kolman

Articles

It is a well-known homological fact that every Abelian groupGhas the property that Hom(G,−)com-mutes with direct products. Here we investigate the ‘dual’ property: an Abelian groupGis said to be cosmallif Hom(−,G)commutes with direct products. We show that cosmall groups are cotorsion-free and that nogroup of cardinality less than a strongly compact cardinal can be cosmall. In particular, if there is a properclass of strongly compact cardinals, then there are no cosmall group

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On Cosmall Abelian Groups, Brendan Goldsmith, O. Kolman Jan 2007

On Cosmall Abelian Groups, Brendan Goldsmith, O. Kolman

Articles

It is a well-known homological fact that every Abelian group G has the property that Hom(G,−) commutes with direct products. Here we investigate the ‘dual’ property: an Abelian group G is said to be cosmall if Hom(−,G) commutes with direct products. We show that cosmall groups are cotorsion-free and that no group of cardinality less than a strongly compact cardinal can be cosmall. In particular, if there is a proper class of strongly compact cardinals, then there are no cosmall groups.

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Hamiltonian Formulation, Nonintegrability And Local Bifurcations For The Ostrovsky Equation, S. Roy Choudhury, Rossen Ivanov, Yue Liu Jan 2007

Hamiltonian Formulation, Nonintegrability And Local Bifurcations For The Ostrovsky Equation, S. Roy Choudhury, Rossen Ivanov, Yue Liu

Articles

The Ostrovsky equation is a model for gravity waves propagating down a channel under the influence of Coriolis force. This equation is a modification of the famous Korteweg-de Vries equation and is also Hamiltonian. However the Ostrovsky equation is not integrable and in this contribution we prove its nonintegrability. We also study local bifurcations of its solitary waves.

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Counting Pill Combinations, David R. Duncan, Bonnie H. Litwiller Jan 2007

Counting Pill Combinations, David R. Duncan, Bonnie H. Litwiller

Faculty Work

Teachers are always on the lookout for problems which combine simple computation and related analyses. We shall present a medication setting which involves these elements.

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Playing Games To Build Understanding, Michele Carnahan, Bridgette Stevens Jan 2007

Playing Games To Build Understanding, Michele Carnahan, Bridgette Stevens

Faculty Work

I am fortunate. I teach from Investigations in Number, Data, and Space [TERC] (1996), a standards-based elementary mathematics curriculum. My evolution from teaching in a traditional teacher-centered approach to one that supports a student-centered community of learners has been a slow and gradual process during the past six years of teaching. Fortunately, through experience, professional development, and graduate level courses, I have come to appreciate the conceptual understanding students acquire from learning mathematics via a student-centered approach and how playing games is an effective instructional strategy for learning mathematics. As intended by the authors of Investigations and envisioned by the …

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Fourier Transform Of Bernstein–Bézier Polynomials, Tian-Xiao He, Charles Chui, Qingtang Jiang Jan 2007

Fourier Transform Of Bernstein–Bézier Polynomials, Tian-Xiao He, Charles Chui, Qingtang Jiang

Scholarship

Explicit formulae, in terms of Bernstein–Bézier coefficients, of the Fourier transform of bivariate polynomials on a triangle and univariate polynomials on an interval are derived in this paper. Examples are given and discussed to illustrate the general theory. Finally, this consideration is related to the study of refinement masks of spline function vectors.

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Clarifications Of Rule 2 In Teaching Geometric Dimensioning And Tolerancing, Cheng Lin, Alok Verma Jan 2007

Clarifications Of Rule 2 In Teaching Geometric Dimensioning And Tolerancing, Cheng Lin, Alok Verma

Engineering Technology Faculty Publications

Geometric dimensioning and tolerancing is a symbolic language used on engineering drawings and computer generated three-dimensional solid models for explicitly describing nominal geometry and its allowable variation. Application cases using the concept of Rule 2 in the Geometric Dimensioning and Tolerancing (GD&T) are presented. The rule affects all fourteen geometric characteristics. Depending on the nature and location where each feature control frame is specified, interpretation on the applicability of Rule 2 is quite inconsistent. This paper focuses on identifying the characteristics of a feature control frame to remove this inconsistency. A table is created to clarify the confusions for students …

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World Bank -Cpa Conflict: The Struggle To Define Human Rights And Development In The Philippines, Adam B. Robbins Jan 2007

World Bank -Cpa Conflict: The Struggle To Define Human Rights And Development In The Philippines, Adam B. Robbins

Honors Theses

This thesis analyzes the interactions between the World Bank (hereafter, the Bank) and the Cordillera Peoples Alliance (CPA), an indigenous and environmental advocacy group based in the Cordillera region of Luzon, in the Philippines. Using data gathered through both text-based and participatory research methods, I analyze the discursive relationship and violent confrontations between the two organizations. Conflicting development and human rights values cause the majority of these conflicts. I focus on how each organization enacts development and human rights, and how this leads to conflict. Ultimately, I intend for this thesis to offer practical guidance for the reader involved in …

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Connecting Polygonizations Via Stretches And Twangs, Mirela Damian, Robin Flatland, Joseph O'Rourke, Suneeta Ramswami Jan 2007

Connecting Polygonizations Via Stretches And Twangs, Mirela Damian, Robin Flatland, Joseph O'Rourke, Suneeta Ramswami

Computer Science: Faculty Publications

We show that the space of polygonizations of a fixed planar point set S of n points is connected by O(n2 ) “moves” between simple polygons. Each move is composed of a sequence of atomic moves called “stretches” and "twangs". These atomic moves walk between weakly simple "polygonal wraps" of S. These moves show promise to serve as a basis for generating random polygons.

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Consistent Estimation With Weak Instruments In Panel Data, Chihwa Kao, Long Liu Jan 2007

Consistent Estimation With Weak Instruments In Panel Data, Chihwa Kao, Long Liu

Center for Policy Research

This note analyzes the asymptotic distribution for instrumental variables regression for panel data when the available instruments are weak. We show that consistency can be established in panel data.

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Statistical Models For Hot Electron Degradation In Nano-Scaled Mosfet Devices, Suk Joo Bae, Seong-Joon Kim, Way Kuo, Paul H. Kvam Jan 2007

Statistical Models For Hot Electron Degradation In Nano-Scaled Mosfet Devices, Suk Joo Bae, Seong-Joon Kim, Way Kuo, Paul H. Kvam

Department of Math & Statistics Faculty Publications

In a MOS structure, the generation of hot carrier interface states is a critical feature of the item's reliability. On the nano-scale, there are problems with degradation in transconductance, shift in threshold voltage, and decrease in drain current capability. Quantum mechanics has been used to relate this decrease to degradation, and device failure. Although the lifetime, and degradation of a device are typically used to characterize its reliability, in this paper we model the distribution of hot-electron activation energies, which has appeal because it exhibits a two-point discrete mixture of logistic distributions. The logistic mixture presents computational problems that are …

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Degradation Models And Implied Lifetime Distributions, Suk Joo Bae, Way Kuo, Paul H. Kvam Jan 2007

Degradation Models And Implied Lifetime Distributions, Suk Joo Bae, Way Kuo, Paul H. Kvam

Department of Math & Statistics Faculty Publications

In experiments where failure times are sparse, degradation analysis is useful for the analysis of failure time distributions in reliability studies. This research investigates the link between a practitioner's selected degradation model and the resulting lifetime model. Simple additive and multiplicative models with single random effects are featured. Results show that seemingly innocuous assumptions of the degradation path create surprising restrictions on the lifetime distribution. These constraints are described in terms of failure rate and distribution classes.

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Centers And Shore Points In Λ-Dendroids, Van C. Nall Jan 2007

Centers And Shore Points In Λ-Dendroids, Van C. Nall

Department of Math & Statistics Faculty Publications

A dendroid is the disjoint union of the set of centers and the set of shore points. We show this is also true for λ-dendroids and use this fact to show that the finite union of shore continua in a λ-dendroid is a shore set.

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An Observation About Frostman Shifts, William T. Ross, Alec L. Matheson Jan 2007

An Observation About Frostman Shifts, William T. Ross, Alec L. Matheson

Department of Math & Statistics Faculty Publications

A classical theorem of Frostman says that if B is a Blaschke product (or any inner function), then its Frostman shifts Bw = (B − w)(1 – w­­¯B)−1 are Blaschke products for all |w| < 1 except possibly for w in a set of logarithmic capacity zero. If B is a Frostman Blaschke product, equivalently an inner multiplier for the space of Cauchy transforms of measures on the unit circle, we show that for all |w| < 1, Bw is indeed another Frostman Blaschke product.

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Stochastic Comparisons Of Parallel Systems When Component Have Proportional Hazard Rates, Subhash C. Kochar, Maochao Xu Jan 2007

Stochastic Comparisons Of Parallel Systems When Component Have Proportional Hazard Rates, Subhash C. Kochar, Maochao Xu

Mathematics and Statistics Faculty Publications and Presentations

Let Χ1, … Χn be independent random variables with Χᵢ having survival function Fλᵢ, i=1, … , n, and let Y₁, … , Yn be a random sample with common population survival distribution Fλ, where λ = Σᵢ=₁nλᵢl n. Let Χn:n and Yn:n denote the lifetimes of the parallel systems consisting of these components, respectively. It is shown that Xn:n is greater than Yn:n in terms of likelihood ratio order. It is also proved that the sample range Χn:n - Χ₁:n is larger than Yn n:n - Y₁:n according to reverse hazard rate ordering. These two results …

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Water Waves And Integrability, Rossen Ivanov Jan 2007

Water Waves And Integrability, Rossen Ivanov

Articles

The Euler’s equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler’s equations is taken (to a certain order of smallness of the scale parameters), relations to certain integrable equations emerge. Some recent results concerning the use of integrable equation in modeling the motion of shallow water waves are reviewed in this contribution.

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On Groups Of Homological Dimension One, Jonathan Cornick Jan 2007

On Groups Of Homological Dimension One, Jonathan Cornick

Publications and Research

It has been conjectured that the groups of homological dimension one are precisely the nontrivial locally free groups. Some algebraic, geometric and analytic properties of any potential counter example to the conjecture are discussed.

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Lessons Learned From The 1918-1919 Influenza Pandemic In Minneapolis And St. Paul, Minnesota, Miles Q. Ott, Shelly F. Shaw, Richard N. Danila, Ruth Lynfield Jan 2007

Lessons Learned From The 1918-1919 Influenza Pandemic In Minneapolis And St. Paul, Minnesota, Miles Q. Ott, Shelly F. Shaw, Richard N. Danila, Ruth Lynfield

Statistical and Data Sciences: Faculty Publications

No abstract provided.

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Hadron Models And Related New Energy Issues, Florentin Smarandache Jan 2007

Hadron Models And Related New Energy Issues, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The present book covers a wide-range of issues from alternative hadron models to their likely implications in New Energy research, including alternative interpretation of lowenergy reaction (coldfusion) phenomena. The authors explored some new approaches to describe novel phenomena in particle physics. M Pitkanen introduces his nuclear string hypothesis derived from his Topological Geometrodynamics theory, while E. Goldfain discusses a number of nonlinear dynamics methods, including bifurcation, pattern formation (complex GinzburgLandau equation) to describe elementary particle masses. Fu Yuhua discusses a plausible method for prediction of phenomena related to New Energy development. F. Smarandache discusses his unmatter hypothesis, and A. Yefremov …

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Lipschitz Continuity And Gateaux Differentiability Of The Best Approximation Operator In Vector-Valued Chebyshev Approximation, Martin Bartelt, John Swetits Jan 2007

Lipschitz Continuity And Gateaux Differentiability Of The Best Approximation Operator In Vector-Valued Chebyshev Approximation, Martin Bartelt, John Swetits

Mathematics & Statistics Faculty Publications

When G is a finite-dimensional Haar subspace of C ( X, Rk), the vector-valued functions (including complex-valued functions when k is 2) frorn a finite set X to Euclidean k-dimensional space, it is well-known that at any function f in C ( X, Rk) the best approximation operator satisfies the Strong Unicity condition of order 2 and a Lipschitz (Holder) condition of order 1/2. This note shows that in fact the best approximation operator satisfies the usual Lipschitz condition of order 1 and has a Gateaux derivative on a dense set of functions in C …

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Some Observations On Khovanskii's Matrix Methods For Extracting Roots Of Polynomials, James Mclaughlin, B. Sury Jan 2007

Some Observations On Khovanskii's Matrix Methods For Extracting Roots Of Polynomials, James Mclaughlin, B. Sury

Mathematics Faculty Publications

In this article we apply a formula for the n-th power of a 3×3 matrix (found previously by the authors) to investigate a procedure of Khovanskii’s for finding the cube root of a positive integer. We show, for each positive integer α, how to construct certain families of integer sequences such that a certain rational expression, involving the ratio of successive terms in each family, tends to α 1/3 . We also show how to choose the optimal value of a free parameter to get maximum speed of convergence. We apply a similar method, also due to Khovanskii, to a …

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Symmetry And Specializability In The Continued Fraction Expansions Of Some Infinite Products, James Mclaughlin Jan 2007

Symmetry And Specializability In The Continued Fraction Expansions Of Some Infinite Products, James Mclaughlin

Mathematics Faculty Publications

Let f(x) ∈ Z[x]. Set f0(x) = x and, for n ≥ 1, define fn(x) = f(fn−1(x)). We describe several infinite families of polynomials for which the infinite product Y∞ n=0 ( 1 + 1 fn(x) ) has a specializable continued fraction expansion of the form S∞ = [1; a1(x), a2(x), a3(x), . . . ], where ai(x) ∈ Z[x] for i ≥ 1. When the infinite product and the continued fraction are specialized by letting x take integral values, we get infinite classes of real numbers whose regular continued fraction expansion is predictable. We also show that, under some …

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Some Properties Of The Distribution Of The Numbers Of Points On Elliptic Curves Over A Finite Prime Field, Saiying He, James Mclaughlin Jan 2007

Some Properties Of The Distribution Of The Numbers Of Points On Elliptic Curves Over A Finite Prime Field, Saiying He, James Mclaughlin

Mathematics Faculty Publications

Let p ≥ 5 be a prime and for a, b ∈ Fp, let Ea,b denote the elliptic curve over Fp with equation y 2 = x 3 + a x + b. As usual define the trace of Frobenius ap, a, b by #Ea,b(Fp) = p + 1 − ap, a, b. We use elementary facts about exponential sums and known results about binary quadratic forms over finite fields to evaluate the sums P t∈Fp ap, t, b, P t∈Fp ap, a, t, Pp−1 t=0 a 2 p, t, b, Pp−1 t=0 a 2 p, a, t and Pp−1 …

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Some More Long Continued Fractions, I, James Mclaughlin, Peter Zimmer Jan 2007

Some More Long Continued Fractions, I, James Mclaughlin, Peter Zimmer

Mathematics Faculty Publications

In this paper we show how to construct several infinite families of polynomials D(¯x, k), such that p D(¯x, k) has a regular continued fraction expansion with arbitrarily long period, the length of this period being controlled by the positive integer parameter k. We also describe how to quickly compute the fundamental units in the corresponding real quadratic fields.

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Continued Fractions With Multiple Limits, Douglas Bowman, James Mclaughlin Jan 2007

Continued Fractions With Multiple Limits, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

For integers m ≥ 2, we study divergent continued fractions whose numerators and denominators in each of the m arithmetic progressions modulo m converge. Special cases give, among other things, an infinite sequence of divergence theorems, the first of which is the classical Stern-Stolz theorem. We give a theorem on a class of Poincar´e type recurrences which shows that they tend to limits when the limits are taken in residue classes and the roots of their characteristic polynomials are distinct roots of unity. We also generalize a curious q-continued fraction of Ramanujan’s with three limits to a continued fraction with …

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Ramanujan And Extensions And Contractions Of Continued Fractions, James Mclaughlin, Nancy Wyshinski Jan 2007

Ramanujan And Extensions And Contractions Of Continued Fractions, James Mclaughlin, Nancy Wyshinski

Mathematics Faculty Publications

If a continued fraction K∞n=1an/bn is known to converge but its limit is not easy to determine, it may be easier to use an extension of K∞n=1an/bn to find the limit. By an extension of K∞n=1an/bn we mean a continued fraction K∞n=1cn/dn whose odd or even part is K∞n=1an/bn. One can then possibly find the limit in one of three ways: (i) Prove the extension converges and find its limit; (ii) Prove the extension converges and find the limit of the other contraction (for example, the odd part, if K∞n=1an/bn is the even part); (ii) Find the limit of the …

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Estimation And The Stress-Strength Model, Naomi Brownstein Jan 2007

Estimation And The Stress-Strength Model, Naomi Brownstein

HIM 1990-2015

The paper considers statistical inference for R = P(X < Y) in the case when both X and Y have generalized gamma distributions. The maximum likelihood estimators for R are developed in the case when either all three parameters of the generalized gamma distributions are unknown or when the shape parameters are known. In addition, objective Bayes estimators based on non informative priors are constructed when the shape parameters are known. Finally, the uniform minimum variance unbiased estimators (UMVUE) are derived in the case when only the scale parameters are unknown.

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Categorical Properties Of Lattice-Valued Convergence Spaces, Paul Flores Jan 2007

Categorical Properties Of Lattice-Valued Convergence Spaces, Paul Flores

Electronic Theses and Dissertations

This work can be roughly divided into two parts. Initially, it may be considered a continuation of the very interesting research on the topic of Lattice-Valued Convergence Spaces given by Jager [2001, 2005]. The alternate axioms presented here seem to lead to theorems having proofs more closely related to standard arguments used in Convergence Space theory when the Lattice is L = f0; 1g:Various Subcategories are investigated. One such subconstruct is shown to be isomorphic to the category of Lattice Valued Fuzzy Convergence Spaces defined and studied by Jager [2001]. Our principal category is shown to be a topological universe …

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